What is the surface area of this rectangular pyramid? ft 1 ft 1 ft
To find the surface area of a rectangular pyramid, you need to calculate the area of each face and then add them together.
A rectangular pyramid has 5 faces: 1 base and 4 triangular faces.
The base of the pyramid is a rectangle with dimensions 1 ft by 1 ft, so its area is 1 ft * 1 ft = 1 square foot.
The 4 triangular faces are all congruent and have a base equal to the length of one side of the rectangle and a height equal to the slant height of the pyramid.
The slant height can be found using the Pythagorean theorem:
h^2 = l^2 + b^2,
where h is the slant height, l is one side of the rectangle (1 ft), and b is the base of the triangle.
Since the rectangle is a square, l = b = 1 ft.
h^2 = 1^2 + 1^2 = 2
h = √2 ≈ 1.414 ft
Now, we can calculate the area of the 4 triangular faces:
Area of each triangular face = 1/2 * b * h = 1/2 * 1 ft * 1.414 ft = 0.707 square feet
Therefore, the surface area of the rectangular pyramid is:
Surface area = base area + 4 * triangular face area
Surface area = 1 ft^2 + 4 * 0.707 ft^2 = 1 ft^2 + 2.828 ft^2 = 3.828 square feet.